Yes, we replaced 1939 3/8" partial inset cabinets when we remodeled (and still have them in one bathroom). Those definitely stick, though I think that's as much about the many layers of paint on them as it is about the style.

@Kim Hasty here are ours--though it's very hard to get both types in the same photo!

And a better photo of the inset side (fridge has since been replaced):